The Vatican is no ordinary state, and the pope's trip to Britain this month will be no ordinary state visit. No other leader who comes to these shores takes time out between the official meetings and dinners to conduct a beatification, as Benedict XVI plans to do. None, probably not even the president of the United States, would expect to draw the same crowds, attract the same adulation – or stir the same resentment. It will be a big deal. The gathering storm over the cost of £10m or so to the taxpayer needs to be placed in that context. Proselytising atheists are encouraging public resentment against the expense of policing the pope's visit, and yet the same gang are inflaming these costs by suggesting that they will try to arrest him. The financial argument is a distraction, a mere veil for deeply held feelings about whether or not it is right for Whitehall to roll out the red carpet for the world's greatest theocrat.

The moral case against Benedict is powerful – and persuasive. For all the admirable work against poverty that Roman Catholicism inspires around the world, the church directly aggravates the plight of vulnerable people. It rails against IVF giving children to the childless, against stem-cell research giving hope to the sick, and against the use of condoms – even as a means of preventing the spread of HIV. Its rigid views on homosexuality and the role of women are not unique in world religion, or even within Christianity, but the extent of child abuse for which its priests have been responsible has been shocking, as has its tendency to close ranks in response to the scandal. Benedict himself, an arch-conservative, has in the past manoeuvred to preserve the autonomy of the church in such matters, as opposed to having them immediately handed on to the police. He has also indulged the standing of Catholic figures who have turned a blind eye to Nazi atrocities.

A case against Benedict, however, is not the same thing as a case against allowing him a state visit. All manner of tyrants have been welcomed to London over the years, and – to take one example – the human rights record of China, which is uniformly dismal where the Vatican's is mixed, was no bar to President Hu Jintao enjoying a grand trip in 2005. Purists would make a stand against flattering thuggery in all circumstances, but most of the rationalistic punters protesting against the pope's visit would accept that peace and prosperity often rely on dealing with power as we find it, as opposed to power as we might like it to be. The argument then comes down to claiming that the Vatican is not a proper state, a point recently run by the philosopher AC Grayling, who speculated on what treatment world leaders would give him if he declared his south London garden a nation.

There is, perhaps, an echo here of Stalin's contemptuous question about how many divisions the pope had. As a matter of fact the pope is a head of state, one that conducts diplomatic relations with 178 capitals around the world. As a matter of what foreign-affairs wonks label soft power, he is a force that cannot be ignored. The spiritual leader of a billion people around the world is, for better or worse, somebody with clout. The Catholic church flexed malign muscle within our own politics a few years ago by forcing Labour ministers to drop a scheme that would have encouraged a measure of religious mixing in faith schools. But it has been a force for good, too, in securing the writing-down of poor countries' debt, and is increasingly a useful voice on climate change. London is right to recognise that the pope is in a better position to protect the Brazilian rainforest than the Foreign Office.

The pope could come in a purely pastoral as opposed to diplomatic capacity, as his predecessor did in 1982. Even so, the last pontiff's arrival was said to have coincided with brief restraint in the Falklands war, and the truth this time is that there is serious diplomacy to do. Unattractive as the holy visitor is in so many respects, his trip is wholly justified.